The following correction was printed in the Guardian's Corrections and clarifications column, Monday May 2 2005

The warning from US scientists that warming at the present rate over 10,000 years would cause sea levels to rise by a kilometre is mathematically correct but physically impossible. We omitted a qualifying statement from the Nasa briefing paper which said "if there were that much ice".

The world is getting warmer - and US scientists now know precisely how much warmer. They calculated the radiation from the sun, the heat reflected back into space, and the rising temperature of the seas and say the extra warmth is equivalent to a 1 watt lightbulb shining constantly over an area of 1 sq metre everywhere on the planet.

That would raise average temperatures by 0.6C before the end of the century, they report in Science today. Warming at that level, maintained over 10,000 years, would melt enough ice to raise sea levels by a kilometre.

"This energy imbalance is the smoking gun that we have been looking for," said James Hansen, director of Nasa's Goddard Institute for Space Studies. "It shows that our estimates of the human-made and natural climate forcing agents are about right, and they are driving the Earth to a warmer climate."

Most of the world - with the exception of the US and Australia - has signed up to the Kyoto protocol to limit greenhouse gas emissions and further global warming. The US government has repeatedly argued that scientific opinion about global warming is divided. With this new research, US government-funded scientists have once again told the US administration that they believe global warming is real, and inexorable.

Computer models of future global warming suggest that planetary temperatures could rise by as much as 5.8C in the next century, with sea level rises of a metre. Since 1993, the world's oceans have risen at the rate of 3.2cm per decade. This is twice the sea level rise of the last 100 years. The warmer the oceans, the faster the planet's ice sheets will melt.

"We need to monitor the ice sheets and sea level precisely to be sure that the system is not running out of our control," Dr Hansen said.